FiltrationValue Struct Reference

Value type for a filtration function on a cell complex. More...

Public Member Functions

bool operator< (FiltrationValue f1, FiltrationValue f2)
 Operator < is a StrictWeakOrdering.
 

Detailed Description

Value type for a filtration function on a cell complex.

A filtration of a cell complex (see FilteredComplex) is a function \(f:\mathbf{K} \rightarrow \mathbb{R}\) satisfying \(f(\tau)\leq f(\sigma)\) whenever \(\tau \subseteq \sigma\). Ordering the simplices by increasing filtration values (breaking ties so as a simplex appears after its subsimplices of same filtration value) provides an indexing scheme (see IndexingTag).

Examples:
Alpha_complex/alpha_complex_3d_persistence.cpp, Alpha_complex/alpha_complex_persistence.cpp, Alpha_complex/exact_alpha_complex_3d_persistence.cpp, Alpha_complex/periodic_alpha_complex_3d_persistence.cpp, Alpha_complex/weighted_alpha_complex_3d_persistence.cpp, Alpha_complex/weighted_periodic_alpha_complex_3d_persistence.cpp, Bottleneck_distance/alpha_rips_persistence_bottleneck_distance.cpp, Persistent_cohomology/persistence_from_file.cpp, Persistent_cohomology/persistence_from_simple_simplex_tree.cpp, Persistent_cohomology/rips_multifield_persistence.cpp, Persistent_cohomology/rips_persistence_step_by_step.cpp, Persistent_cohomology/rips_persistence_via_boundary_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_distance_matrix.cpp, Rips_complex/example_one_skeleton_rips_from_points.cpp, Rips_complex/example_rips_complex_from_csv_distance_matrix_file.cpp, Rips_complex/example_rips_complex_from_off_file.cpp, Rips_complex/rips_distance_matrix_persistence.cpp, Rips_complex/rips_persistence.cpp, Simplex_tree/cech_complex_cgal_mini_sphere_3d.cpp, Simplex_tree/simple_simplex_tree.cpp, Simplex_tree/simplex_tree_from_cliques_of_graph.cpp, Witness_complex/strong_witness_persistence.cpp, and Witness_complex/weak_witness_persistence.cpp.

The documentation for this struct was generated from the following file:
GUDHI  Version 2.2.0  - C++ library for Topological Data Analysis (TDA) and Higher Dimensional Geometry Understanding.  - Copyright : GPL v3 Generated on Thu Jun 14 2018 15:00:55 for GUDHI by Doxygen 1.8.13